Extending Distance Geometry methods: not only distances (A study of three applications with a focus on structural biology)

We study different aspects of the Distance Geometry Problem (DGP). The DGP is an inverse problem where a set of pairwise distances is inverted to find a structure in a Euclidean space, given a certain dimension K. Our main focus lies on the application of structural biology, where we can exploit inter-atomic distances to compute protein structures. For this application, we are able to discretize the search space using branch-and-prune methods. We extend the method to not only use distance information but also torsion angles. We present experiments using real NMR data with promising results. Next, we look at dynamical Distance Geometry with a main focus on human motions, laying the groundwork for future projects which could focus on modeling protein dynamics. Furthermore, we discuss adaptive maps, which is another example of an application of DG in which we can exploit more than just distance information.